If the roots of the equation b x² + cx + a = 0 imaginary, then for all real values of x, the expression 3b²x² + 6bcx + 2c² is:

Complex Numbers and Quadratic Equations: JEE Main 2009 Mathematics question

JEE Main 2009 · Annual, Paper 1 · Q5090

JEE Main 2009Annual, Paper 1MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

If the roots of the equation

b{x^2} + cx + a = 0

imaginary, then for all real values of

x

, the expression

3{b^2}{x^2} + 6bcx + 2{c^2}

is :